Orbit-based dynamical models of the Sculptor dSph galaxy

Abstract

We have developed spherically symmetric dynamical models of dwarf spheroidal galaxies using Schwarzschild's orbit superposition method. This type of modelling yields constraints both on the total mass distribution (e.g. enclosed mass and scale radius) as well as on the orbital structure of the system (e.g. velocity anisotropy). This method is thus less prone to biases introduced by assumptions in comparison to the more commonly used Jeans modelling, and it allows us to derive the dark matter content in a robust way. Here we present our results for the Sculptor dwarf spheroidal galaxy, after testing our methods on mock data sets. We fit both the second and fourth velocity moment profile to break the mass-anisotropy degeneracy. For an NFW dark matter halo profile, we find that the mass of Sculptor within 1 kpc is M 1kpc = (1.03 ± 0.07) × 10 8 M ⊙ , and that its velocity anisotropy profile is tangentially biased and nearly constant with radius. The preferred concentration (c ∼ 15) is low for its dark matter mass but consistent within the scatter found in N-body cosmological simulations. When we let the value of the central logarithmic slope α vary, we find that the best-fit model has α = 0, although an NFW cusp or shallower is consistent at 1σ confidence level. On the other hand, very cuspy density profiles with logarithmic central slopes α < −1.5 are strongly disfavoured for Sculptor.

A discrete chemo-dynamical model of the dwarf spheroidal galaxy Sculptor: mass profile, velocity anisotropy and internal rotation

“…There is still considerable debate as to whether the central regions of such halos are cored or cusped (e.g. Kleyna et al 2002;Koch et al 2007;Walker & Peñarrubia 2011;Agnello & Evans 2012;Amorisco & Evans 2012b;Breddels et al 2013). dSphs provide an unprecedented opportunity to test the inner structure of dark matter (DM) halos as they are DM-dominated at all radii and they are dust free (e.g.…”

“…The dashed vertical line indicates the position of the half-light radius r h . Right panel: again the black solid and dashed curves are our mass profiles for the generalised NFW halo, the yellow and green thick curves are the mass profiles of the cored and cusped halos respectively obtained by a two-component spherical Michie-King model (Amorisco & Evans 2012b), the orange line is obtained by a spherical Schwarzschild model with a generalised NFW DM halo (Breddels et al 2013).…”

“…It is still debated whether Sculptor is radially anisotropic or tangentially anisotropic (e.g., Breddels et al 2013;Amorisco & Evans 2012b). In a spherical model,…”

“…Even so, the metal-rich population being more radial anisotropic than the metal-poor population is consistent with our findings. Breddels et al (2013) created single-component orbitbased Schwarzschild models of Sculptor. They binned the data in radius assuming a single population, and showed that the LOS velocity distribution of Sculptor deviates from a Gaussian distribution: the velocity distributions for the bins at small radii have a narrow peak, while the velocity distributions are more flat-topped for the bins in the outskirts.…”

An analytic distribution function for a mass-less cored stellar system in a cuspy dark-matter halo

“…More recently, the application of the Schwarzschild modeling technique to dSph has allowed considerating more general density profiles (e.g., Jardel & Gebhardt 2012;Breddels et al 2013;Jardel et al 2013;. In this approach the distribution functions are obtained in a numerical fashion, and by construction, they are positive everywhere.…”